A graph is said to be Hamiltonian if it contains a spanning cycle. The spanning cycle is called a Hamiltonian cycle of G and G is said to be a Hamiltonian graph. A Hamiltonian path is a path that contains all the vertices in V(G) but does not return to the vertex in which it began. A graph G is said to be hypo hamiltonian if for each vV (G), the vertex sub graph G-v is Hamiltonian. This paper shall prove that every hypo hamiltonian graph G is Hamiltonian if we make the degree of removable vertex V exactly equal to n - 1, that is,   and illustrate it by some counter examples.

Key words: Graphs vertex, Hamiltonian cycle, degree.